No there is not some magic number that gets your accepted. However I've suggested to many that you should have a blog that is 6 months or older and to be able to demonstrate to Google that you've been adding content for the past 6 months on a regular basis (2-3 times a week). Anybody that has followed my advice now has an Adsense account, when they were turned down numerous times before for lack of content.

As for if Adsense is compatible with the other ad network, you'll have to read the policies of Adsense and determine if any of them are breaking the rules or may break the rules that you can anticipate. Such as if the ad network has ads that as publishers we're not allowed to display either because of the content of the ad, or what website the ads may link to, or any other violation.